Horizontal cross-sections (parallel to the base) are rectangular similar to the base itself.
Vertical cross-sections at right angles to a side of the base are trapezoids. Such a one through the apex the trapezoid becomes a triangle. A cross-section through the apex and along a diagonal of the base also produces a triangle. And a trapezoid is also produced by any plane cutting across the rectangular base.
If the cut only includes two adjacent sides of the base the cross-section is a triangle.
If the pyramid is sliced by a plane at an angle to the horizontal, the result is a rectangular cross-section.
Therefore, it seems that the cross-sections are rectangles, trapezoids or triangles.